Theorems · Theorem · logic and foundations
Set.ncard_sdiff_singleton_add_one
∀ {α : Type u_1} {s : Set α} {a : α},
a ∈ s → autoParam s.Finite Set.ncard_sdiff_singleton_add_one._auto_1 → (s \ {a}).ncard + 1 = s.ncard- Defined in
- Mathlib.Data.Set.Card
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 99 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- ENatproof · cited by 4,985
- Nat.cast_oneproof · cited by 2,501
- Set.Finitestatement and proof · cited by 1,814
- Nat.cast_addproof · cited by 586
- Set.ncardstatement and proof · cited by 344
- Set.encardproof · cited by 327
- Nat.cast_injproof · cited by 70
- Set.Finite.cast_ncard_eqproof · cited by 28
- Set.Finite.sdiffproof · cited by 15
- Set.encard_sdiff_singleton_add_oneproof · cited by 6
Cited by3
Results whose statement or proof uses this declaration.
- Set.ncard_sdiff_singleton_of_memproof · cited by 2
- Set.ncard_sdiff_singleton_lt_of_memproof · cited by 1
- Set.ncard_diff_singleton_add_oneproof · cited by 0